Upper and lower bounds for evaluation of nonlinear fracture parameters

Abstract

Bound theorems for estimating small strain nonlinear fracture parameters are proposed. It is found that the lower bound for the J-integral can be obtained by a compatible displacement finite element method. On the other hand, the upper bound of the I*-integral, which is the dual counterpart of the J-integral, can be obtained by an equilibrium finite element method. To verify the theorems and avoid the difficulty of designing equilibrium finite element models, the popular Pian-Sumihara hybrid stress model is modified by incorporating a penalty-equilibrium constraint. Moreover, an incremental formulation of the I*-integral for nonlinear finite element computation is developed. Numerical examples on different crack and loading configurations are presented. All the results indicate the validity of the theorems. © 1999 Elsevier Science Ltd. All rights reserved.